Stability properties of a resonant cascade laser

Valcárcel, Germán J. de; Roldán, Eugenio; Vilaseca, R.

doi:10.1103/physreva.49.1243

Cited by 14 publications

(7 citation statements)

References 32 publications

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“…[20] we showed that the Hopf bifurcation is supercritical (subcritical) and consequently the Hopf orbits are stable (unstable) in the vicinity of HB whenever the quantity [L(p, "n) -2i aio 8]u22= -N( p HB; r, r),…”

Section: Degenerate Tpl Modelmentioning

confidence: 92%

“…In the perfectly tuned case (5 = 0) it reads Eqs. (10) only contain second-order nonlinearities and thus (20) is exact in our case.…”

Section: Degenerate Tpl Modelmentioning

confidence: 95%

“…We address the reader to the Appendix of Ref. [20] and to the book of Iooss and Joseph [32] for details.…”

Section: Degenerate Tpl Modelmentioning

confidence: 99%

“…Ei I, yi l~l x) 7= Pgt , =~,~r i b= ri~~Vi (X is the relative efficiency of the two atomic transitions for one-photon amplification [20], g is the effective two-photon gain parameter, r is the pump parameter, and e, o. , and b…”

Section: Introductionmentioning

confidence: 99%

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Two-photon laser dynamics

et al. 1995

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Degenerate as well as nondegenerate three-level two-photon laser (TPL) models are derived. In the limit of equal cavity losses for both fields, it is shown that the nondegenerate model reduces to the degenerate one. We also demonstrate the isomorphism existing between our degenerate TPL model and that of a dressed-state TPL.All these models contain ac-Stark and population-induced shifts at difference from effective Hamiltonian models. The influence of the parameters that control these shifts on the nonlinear dynamics of a TPL is investigated. In particular, the stability of the periodic orbits that arise at the Hopf bifurcation of the system and the extension of the self-pulsing domains of the system are studied, revealing the role played by the detuning and ac-Stark parameters.PACS number(s): 42.50.Ne, 42.60.Mi, 47.20.Ky

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Section: Degenerate Tpl Modelmentioning

confidence: 92%

“…In the perfectly tuned case (5 = 0) it reads Eqs. (10) only contain second-order nonlinearities and thus (20) is exact in our case.…”

Section: Degenerate Tpl Modelmentioning

confidence: 95%

“…We address the reader to the Appendix of Ref. [20] and to the book of Iooss and Joseph [32] for details.…”

Section: Degenerate Tpl Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Two-photon laser dynamics

et al. 1995

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“…Esta información se puede ampliar con el estudio analítico de la estabilidad de las soluciones periódicas que sabemos que existen en la bifurcación de Hopf [7]. Sin embargo, esto queda fuera del alcance de la práctica que proponemos en el curso y que presentamos en este artículo.…”

Section: Banálisis De Estabilidad De Las Soluciones No Trivialesunclassified

Didactic application of numerical analysis in nonlinear dynamics: Lorenz model study

García-Ferrer¹,

Roldán²,

Silva³

et al. 2017

Opt. Pura Apl.

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ABSTRACT:We describe a practice designed for the numerical study of the Lorenz model that is a central model in the physics of lasers. The didactical objectives pursued in this practice have a dual nature, considering both the introduction to the knowledge of a physical paradigm of deterministic chaos as the training for the use of certain computational tools for its characterization. The method used to achieve programming is finding solutions of the Lorenz model and systematically studying of their temporal evolution using a Mathematica program. In the academic context, the practice is designed to be included in the curriculum of the degree in physics and to facilitate adaptation to other matters in this area, such as quantum optics, fluids, mechanical vibrations, etc. We first study the steady states, and their linear stability, of the Lorenz model equations and then numerically study the different types of dynamic behavior. We pay special attention to the deterministic chaotic behavior and to the sequence of bifurcations leading from periodic to chaotic behavior (routes to chaos).Key words: Lorenz model, chaos, nonlinear dynamics, laser, didactic, Mathematica. RESUMEN:Describimos una práctica diseñada para el estudio numérico de un modelo central en la física del láser, el modelo de Lorenz. Los objetivos didácticos que se persiguen en la práctica tienen una naturaleza doble, por un parte, la introducción al conocimiento de un paradigma físico del caos determinista y, por otra, la capacitación para la utilización de ciertas herramientas computacionales que permiten su caracterización. El método utilizado para alcanzarlos es la búsqueda de las soluciones del modelo de Lorenz y el estudio sistemático de su evolución temporal mediante el programa Mathematica. En el contexto académico, la práctica está diseñada para ser incluida en el currículum del grado en Física y para facilitar su adaptación a otras materias dentro de este ámbito, como puede ser óptica cuántica, fluidos, oscilaciones mecánicas, etc. Partiendo de las ecuaciones del modelo de Lorenz, estudiamos sus estados estacionarios y su estabilidad lineal, para después estudiar numéricamente los distintos tipos de comportamiento dinámico. Prestamos especial atención al comportamiento caótico determinista y a la secuencia de bifurcaciones que lleva de los comportamientos periódicos a los caóticos (rutas al caos).Palabras clave: Modelo de Lorenz, caos, dinámica no lineal, láser, didáctica, Mathematica. REFERENCES AND LINKS / REFERENCIAS Y ENLACES[1] E.N. Lorenz, "Deterministic nonperiodic flow", J. Atm. Sci. 20, 130-141 (1963).

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